What is the derivative of f(x)=(3x-7)/(5x-2) ?

The derivative of f(x)=(3x-7)/(5x-2) is (29)/((5x-2)^2)

What is the first derivative of f(x)=(3x-7)/(5x-2) ?

The first derivative of f(x)=(3x-7)/(5x-2) is (29)/((5x-2)^2)

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derivative of

f (x) = \frac{3 x - 7}{5 x - 2}

\frac{29}{( 5 x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x - 7}{5 x - 2})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x - 7 ) ( 5 x - 2 ) - \frac{d}{d x} ( 5 x - 2 ) ( 3 x - 7 )}{( 5 x - 2 ) ^{2}}

\frac{d}{d x} (3 x - 7) = 3

\frac{d}{d x} (5 x - 2) = 5

= \frac{3 ( 5 x - 2 ) - 5 ( 3 x - 7 )}{( 5 x - 2 ) ^{2}}

Expand

3 (5 x - 2) - 5 (3 x - 7) : 29

= \frac{29}{( 5 x - 2 ) ^{2}}

What is the derivative of f(x)=(3x-7)/(5x-2) ?
The derivative of f(x)=(3x-7)/(5x-2) is (29)/((5x-2)^2)
What is the first derivative of f(x)=(3x-7)/(5x-2) ?
The first derivative of f(x)=(3x-7)/(5x-2) is (29)/((5x-2)^2)